This invention relates generally to a method or technique of designing, defining and generating a surface to correspond to a primary surface or to provide an optical device producing desired refraction effects, where the output surface definition is based on analysis of an input surface definition, as well as to such surfaces or optical devices so produced. The method may be utilized to provide control data to various surface generation instruments, such as CNC lathe equipment, laser surfacing equipment and mold generating instruments, for example. It is particularly suitable for producing customized contact lenses of specific surface topographies in response to measurements of the corneal surface.
Optical systems used for ophthalmic purposes, such as for example contact lenses or intraocular lens implants, are designed to provide clear vision when viewing various targets located at different locations in space. In the past, lenses have been designed to optimize a specific range of distances presented from a specific range of angles of view. The task of designing optical surfaces for ophthalmic lenses has been primarily approached by using surface formulas based upon polynomial mathematics which describe curves as a single equation containing numerous variables that can be modified in an attempt to control aberrations at different points across the surface. The results typically included compromises at some point, distance or angle within the overall system to account for the lack of defined precision at particular finite points, meaning that accuracy at any particular point is often sacrificed due to the inability to more precisely define in a mathematical sense the necessary parameters at a given point. Likewise, the known production methodologies typically fail to account for variations in individual corneal surfaces between patients having identical or equivalent vision problems, such that the actual optical corrections provided by lenses designed with the same corrective characteristics will vary relative to each individual patient.
The present method is a method of optical surface design which does not depend on polynomial mathematics for aberration control. In this method, each section of the lens can be designed independently from other areas of the lens. Spherical aberration is an optical defect which describes the fact that light rays entering a refractive surface for focusing, such as the cornea of a human eye, are less strongly focused at the center of the curved refractive surface and are progressively focused more strongly as the distance from the center of the cornea increases. The image is therefore not focused onto a single point on the retina, but is instead focused at multiple focal points short of the intended focal point, which results in blurred vision. The mathematical basis for this method is founded on digital signal processing concepts including the principles of wavelet transform analysis.
It is therefore an object of this invention to provide a method for producing from resulting digital data an output surface, or the definition of an output surface, with desired characteristics based on input data from an input surface or mathematical description, where the method provides a more accurate output surface relative to each point on its surface. It is a further object to provide such a method which is particularly suited to producing accurate optical output surfaces, such as on a contact lens or intraocular lens, based on input derived from the corneal surface of the eye of a patient.
The process involves the steps of first defining a baseline surface from input data derived from or defined as an input surface definition, where the input data may be a result of data generated by testing instrumentation, such as for example topography measurement instruments or wavefront measurement instruments, or a result of mathematical modeling of a surface, such as for example a sphere on an ellipsoid. The input data is formatted by defining an apex as a point on the input surface located on a line which serves as a reference axis that is perpendicular to a plane which tangential to the curvature of the surface at the apex. The input data is then analyzed and formatted into discrete, evenly spaced points across an adequate number of semi-meridians converging at the apex for accuracy, with points on each semi-meridian peripheral to the apex defined in terms of x and z coordinates, with x designating the distance from the reference axis and z designating the distance from a line in the plane perpendicular to the axis that passes through the apex, and a convolution function is performed to create a surface that is smoothed to within a specific threshold of curvatures at any point on the surface. The desired surface characteristics at a particular point on the output surface or the desired optical effect at a particular point on the lens in terms of curvature is then defined. An arbitrary amplitude is assigned to a one quarter wavelength phase range of a sinusoidal function, beginning at either one quarter or three quarter wavelength, and this is added to the source data. The curvature after the initial phase range is added to the source data is then calculated, and a bracketing algorithm is employed to adjust the amplitude of the one quarter wavelength function until the target curvature is obtained. The amount of induced distortion from the resultant data is measured, and an arbitrary value is assigned to a one quarter wavelength of twice the original wavelength and 180 degrees change in phase angle, and the results are added to the first summation. A bracketing algorithm is then utilized to adjust the surface until a minimal amount of distortion is measured in resultant data. The resultant data in digital format thus represents the targeted optical effect, and can be used as input for various surface generation instruments. Thus, for example, topographical data derived from the surface of a patient""s cornea can be manipulated as above to produce a customized contact lens or an intraocular lens for the patient with surface topography matched to the cornea such that optimal optical effects are produced by the lens. The topographical data of the corneal surface can also be utilized, for example, to produce a control mask for laser sculpting of the corneal surface.